Exponential convergence rates for the kernel bivariate distribution function estimator under NSD assumption with application to hydrology data

Abstract

In this paper, we study the asymptotic behavior of the kernel bivariate distribution function estimator for negatively superadditive dependent. The exponential convergence rates for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth rate is determined with respect to mean squared error criteria. A simulation study is used to justify the behavior of the kernel and histogram estimators. As an application, a real data set in hydrology is considered and the kernel bivariate distribution function estimator of the data is investigated.

Keywords:

• Bivariate distribution function
• kernel estimation
• negative superadditive dependence

MSC:

• Primary 62G07
• Secondary 62G20

Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions that improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research has been supported by a grant from Ferdowsi University of Mashhad (No.2/52503).